【LeetCode 0037】【回溯/剪枝】解数独

37. Sudoku Solver

Write a program to solve a Sudoku puzzle by filling the empty cells.

A sudoku solution must satisfy all of the following rules:

• Each of the digits 1-9 must occur exactly once in each row.
• Each of the digits 1-9 must occur exactly once in each column.
• Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.

The '.' character indicates empty cells.

Example 1:

**Input:** board = [["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]
**Output:** [["5","3","4","6","7","8","9","1","2"],["6","7","2","1","9","5","3","4","8"],["1","9","8","3","4","2","5","6","7"],["8","5","9","7","6","1","4","2","3"],["4","2","6","8","5","3","7","9","1"],["7","1","3","9","2","4","8","5","6"],["9","6","1","5","3","7","2","8","4"],["2","8","7","4","1","9","6","3","5"],["3","4","5","2","8","6","1","7","9"]]
**Explanation:** The input board is shown above and the only valid solution is shown below:

<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/3/31/Sudoku-by-L2G-20050714_solution.svg/250px-Sudoku-by-L2G-20050714_solution.svg.png" style="height:250px; width:250px">

Constraints:

• board.length == 9
• board[i].length == 9
• board[i][j] is a digit or '.'.
• It is guaranteed that the input board has only one solution.

JavaScript Solution

/**
 * @param {character[][]} board
 * @return {void} Do not return anything, modify board in-place instead.
 */
var solveSudoku = function(board) {
    solve(board)
    
};
let solve = (board)=>{
    let len = board.length
    for(let row = 0 ; row < len; row ++ ){
        for(let col = 0; col < len; col ++){
            if(board[row][col] == '.'){
                for( let c = 1; c < 10; c++){
                    if(isValid(board,row,col,c)){
                        board[row][col] = String.fromCharCode(48+c)
                        if(solve(board)){
                            return true
                        }else{
                            board[row][col] = '.'
                        }
                    }           
                }
                return false         
            }
        }
    }
    return true
};
let isValid = (board,row,col,c)=>{
    for(let i = 0;i < 9 ;i++){
        if(board[i][col] == c)return false
        if(board[row][i] == c)return false
        if(board[3*Math.floor(row/3) + Math.floor(i/3) ][3*Math.floor(col/3) + (i%3) ] == c)return false
    }
    return true
}